Robert Fathauer

Small business owner, puzzle designer, and artist
Tessellations Company
Phoenix, Arizona
Robert Fathauer makes limited-edition prints inspired by tiling, fractals, and knots. He employs mathematics in his art to express his fascination with certain aspects of our world, such as symmetry, complexity, chaos, and infinity. His artworks are created on a Macintosh computer.
Fractal Tree No. 13
13" x 16"
Digital print
"Fractal Tree No. 13" is a black-and-white digital artwork constructed by graphically iterating a photographic building block. Several photographs of a small portion of a palo verde tree were combined and digitally altered to create the building block, which allows smooth joining of smaller copies to larger copies. In addition to being scaled down, the three smaller copies added with each iteration are rotated by varying angles, and one is reflected as well. A sufficiently large number of iterations were performed so that the image is indistinguishable to the eye from the image that would result after an infinite number of iterations. In this particular tree, the iteration rules result in considerable overlap of the branches, leading to a complex collection of small features reminiscent of pencil marks. The fractal shape of the envelope of these features didn't emerge until approximately one dozen iterations were performed.